## Step 5: Simplifying Fractions

**Simplifying Fractions**

Often after you add, the fraction can be simplified. A fraction whose numerator and denominator both have a factor in common can be simplified. (Factors are numbers that the original number is evenly divisible by, or numbers that can be multiplied to give the original number.)

We can demonstrate this using the results of the two examples in Step 4:

^{6}/

_{9}and 1

^{2}/

_{12}.

If we examine

^{6}/

_{9}, and find the factors of the numerator and the factors of the denominator, we find:

factors of 6: 1, 2, 3, and 6 (because 1 x 6 = 6 and 2 x 3 = 6)

factors of 9: 1, 3, and 9

Since 3 is a common factor of both numbers, we can divide both the numerator and denominator by 3 and get a simplified fraction. As with multiplying both the top and bottom of the fraction by the same number, dividing them each by the same number results in an equivalent, or equal, fraction.

So 6 divided by 3 = 2,

and 9 divided by 3 = 3,

so our resulting simplified fraction =

^{2}/

_{3}.

Likewise with 1

^{2}/

_{12}. Looking at the fractional part of the answer and finding the factors we find:

factors of 2: 1 and 2

factors of 12: 1, 2, 3, 4, 6, and 12

Dividing both the numerator and denominator of our fraction by 2 (the greatest common factor), gives:

2 divided by 2 = 1

12 divided by 2 = 6

so our resulting simplified answer is 1

^{1}/

_{6}.

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